Fracturing of subterranean geological structures can be useful for assisting in the development of hydrocarbon resources from subterranean reservoirs. In certain types of formations, fracturing of a region surrounding a well or borehole can allow for improved flow of reservoir fluids to the well (e.g., oil, water, gas). A conventional method for causing such fracturing in the geologic structure involves generating hydraulic pressure, which may be a static or quasi-static pressure generated in a fluid in the borehole. Another method includes generation of a shock in conjunction with a hydraulic wave by creating an electrical discharge across a spark gap. For example, pairs of opposing electrodes, such as axial, rod, or pin electrodes, have been used to generate electrical discharges. In such electrode designs, the electrodes (e.g., with diameters ranging from 1 millimeter to approximately 1 centimeter) are typically placed apart (e.g., between one half to several centimeters) depending on the application and the voltage. These electrode configurations are typically for low-energy applications.
In higher-energy applications and with the use of conventional electrode configurations, electrode erosion may occur at the tip of the electrode and increase the spacing between the electrodes. Erosion of metal from the electrodes is roughly proportional to the total charge passing through the electrodes for a given electrode material and geometry. This erosion is usually expressed in terms of mass per charge (e.g., milligrams per coulomb, mg/C). Electrode erosion can also be expressed as eroded axial distance of the electrode per charge (e.g., millimeters per coulomb, mm/C). Thus, mass per charge (e.g., mg/C) is converted to eroded axial distance of the electrode per charge (e.g., mm/C) by expressing the eroded mass in terms of the mass of the electrode (i.e., ρ×area×length, where ρ is the density of the electrode material). The table below is an example of measured erosion rates in water for various materials using a 0.32-cm-radius pin (or rod) electrode.
Materialmg/Cmm/kCbrass5.520.74340 steel2.7511.0316 steel2.59.8Hastalloy3.513.4tantalum4.58.5Mallory 20002.54.4tungsten1.52.5Elkonite 50W-311.7
While not shown in the above table, the measured electrode erosion from the negative electrode was in general higher than the positive electrode by approximately 15% to 25%. As the electrode spacing increases, it becomes more difficult to create a breakdown in the medium (e.g., water) between the electrodes and the electrodes are typically adjusted or replaced to reduce the gap.
For a given electrical pulser's specifications (total delivered charge), the eroded electrode length per shot can be determined. Further, by defining the maximum allowed electrode erosion as the maximum permitted increase in the electrode gap, the lifetime of the electrode system between refurbishment can be identified. This results in an erosion formula in which the variables for a given pulser are the electrode material and the electrode radius. Realistically, the maximum electrode radius is limited by both the required geometric, electric-field enhancement (that drops with an increase in the electrode radius) and the proximity of the pin or rod electrode to the grounded wall of the chamber that encloses the arc. The low levels of field enhancement on the high-voltage, large-diameter electrode (and, simultaneously, the ground electrode) cause a significant increase in the delay time between the application of high voltage to the electrodes and the start of current flow in the arc. At the same time, there is a substantial increase in the jitter at the start of current flow.
Furthermore, for long-pulse, high-energy electrical pulsers, the operational radius can be up to approximately one (1) centimeter. With such a radius size, axial electrodes can experience additional issues. For example, the extremely long time duration of the voltage and current pulses permits the development of many pre-arc “streamers” on the electrodes. In an electrode configuration having low electric-field enhancement, these streamers form with nearly equal probability between the high-voltage and ground electrodes and between the high-voltage electrode and any other ground in the system (e.g., the wall of the generator). This physical limit in electrode radius effectively limits the available mass to be eroded with pin-electrode designs and limits the maximum current rise time of a pin electrode design.
Furthermore, the electrode gap can become a major hindrance at very high (e.g., megajoule, MJ) pulser energies. There are applications require electrical pulsers that store electrical energy up to 1 MJ and deliver a large amount of charge to the load. Such applications may also require many hundreds or thousands of shots between refurbishment. Even with excellent electrode materials, the use of simple pin or rod electrodes may not be feasible due to the rapid increase in electrode gap due to electrode erosion. Additionally, the adjustability of the electrodes leads to a primary failure mode and therefore, MJ-class electrode assemblies typically do not provide adjustment capability in order to maximize reliability.
While conventional electrode configurations have been used successfully to form fractures, there is a continued need for an improved method and apparatus for generating high-pressure pulses in a subterranean medium, thereby causing fracturing to occur.